Kelly Criterion: The Risk Formula Nobody Uses FullyBlackRock, Inc.BATS:BLKVertexQoreThere's a mathematical formula that'll tell you exactly what percentage of your account to risk on every trade for optimal long-term growth. It was developed by a scientist at Bell Labs in the 1950s and has been used by professional gamblers and hedge funds alike for decades - it's an approach that most retail traders will never have heard of. Almost none of those who have ever used it employ it in the exact way that it's intended to be used, for sound mathematical reasons. This article discusses what the Kelly Criterion formula actually calculates, how to calculate it, and why you should rarely use the full number generated by this calculation. What the Kelly Criterion formula actually calculates The formula for the Kelly Criterion is as follows: f = W − Wheref is the percentage of your account you should risk on a given trade, W is your win rate (expressed as a decimal), and R is your average win size divided by your average loss size (your reward-to-risk ratio). If your strategy has a 50% win rate (W = 0.5), and your average win size is double your average loss size, your R is 2. Plugging these numbers in gives us: f = 0.50 − = 0.50 − 0.25 = 0.25. According to the Kelly Criterion, you should therefore be risking 25% of your account size on any given trade. That number represents the percentage of your account size that will produce the highest theoretical long-term growth rate, given the exact win rate and reward-to-risk ratio inputs. Why the full Kelly number is often insane to use Twenty-five percent of your account size on any given trade is not a conservative number to risk, and it's not likely to be one that any real-world trader would be comfortable with, even if they've spent years learning about the Kelly formula. It's important to understand why the Kelly Criterion is mathematically optimal - but in the real world, it's far too volatile to actually employ. The biggest issue with the full Kelly number is that it requires you to use the exact full number generated by the formula on every trade you make. Even with a strategy that has a demonstrably positive expected value, fully employing the formula's suggested percentage will generate far more volatility for your account balance than most traders are comfortable with, due to inevitable drawdowns along the way. In some cases, the drawdowns can absolutely exceed 50% of your account balance, simply through normal variance, before the long-term upward trend seen in fully employing the formula takes hold. Most traders, faced with a drawdown of this magnitude, will simply quit out and admit defeat, even though the drawdown was entirely predicted by the Kelly math. There's another reason to avoid the full Kelly number as well - the inputs to the equation are rarely completely accurate, especially if you're using a real-world trading strategy. The win rate and reward-to-risk ratio inputs to the formula are almost always estimates based upon a sample of your strategy's past performance. If you overestimate either of these numbers, the percentage suggested by the formula becomes far riskier than most people expect, with an even higher possibility of ruin during a drawdown than predicted. Why professional traders use Half Kelly This is the part that few people mention about the Kelly Criterion - in practice, almost no professional trader or quant fund actually employs the full percentage suggested by the formula. Instead, most professional traders use Half Kelly, which means taking the full percentage suggested by the Kelly formula and cutting it in half when risking account balance on any given trade. In our earlier example, the full Kelly number suggested risking 25% of your account on any given trade, but Half Kelly would cap the suggested risk at 12.5%. The surprising thing about this approach is that it sacrifices far less theoretical long-term growth than most people realize, while dramatically reducing the possibility of devastating drawdowns that can occur with the full formula. You're taking on less risk for only slightly less theoretical reward, and for most people, that's a far more palatable risk/reward ratio to live with in the real world. Some traders take this approach even further, and use a quarter of the suggested full Kelly number, especially if they've used a smaller sample size when calculating their win rate and reward-to-risk ratio. A simple illustration of why these approaches have value Let's say that we have two identical traders, but one of them employs the full Kelly number when risking account balance on a trade, while the other employs only Half Kelly. Over a sufficiently long period of time and sample size of trades, the trader using the full Kelly number will have a higher theoretical account balance than the trader using Half Kelly. However, this increase in theoretical account value will come at the expense of far greater volatility in the account value from trade to trade (and potentially devastating drawdowns in the interim). The trader using Half Kelly will have a slightly lower theoretical account value, but this value will be far more stable from trade to trade, with normal drawdowns being only about 25% as extreme as the drawdowns seen in the full Kelly account, since the risk taken on each trade is scaled down at a faster rate than the potential reward. For almost any real-world trader, that trade-off between slightly lower theoretical value for far greater stability is worth it. How to calculate the Half (or even Quarter) Kelly number for your own strategy Take your trading strategy's win rate and average reward-to-risk ratio (preferably over at least 50 total past trades) and plug them into the formula: f = W − . Divide the resulting number in half to get a better, more survivable risk percentage for your trades - and if you're unsure of your win rate and reward-to-risk ratio using a smaller sample size, consider dividing the suggested number by four instead. Recalculate this number periodically as your trading strategy performs more trades, since the win rate and reward-to-risk ratio inputs to the formula can change with time, and your account's theoretical value using an out-of-date formula may no longer be accurate for predicting future performance. My Conclusion The Kelly Criterion provides one of the few ways to actually calculate exactly what percentage of your account balance you should be risking on a given trade for maximum long-term theoretical growth. However, the full number provided by the formula is rarely useful for a real-world trader, due to the enormous volatility that can occur in any trading strategy. Using Half, or even a Quarter, of the suggested number is far more palatable for most real people, while still providing a decent approximation for the theoretical long-term account value after many trades have been made. Knowing the formula is useful, but knowing why almost no real-world trader ever employs the full suggested number is far more valuable. Thank you @VertexQore